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        <title>API docs for &ldquo;sympy.matrices.matrices&rdquo;</title>
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        <body><h1 class="module">Module s.m.matrices</h1><span id="part">Part of <a href="sympy.matrices.html">sympy.matrices</a></span><div class="toplevel"><div class="undocumented">Undocumented</div></div><table class="children"><tr class="class"><td>Class</td><td><a href="sympy.matrices.matrices.NonSquareMatrixException.html">NonSquareMatrixException</a></td><td><span class="undocumented">Undocumented</span></td></tr><tr class="class"><td>Class</td><td><a href="sympy.matrices.matrices.ShapeError.html">ShapeError</a></td><td><div><p>Wrong matrix shape</p>
</div></td></tr><tr class="class"><td>Class</td><td><a href="sympy.matrices.matrices.MatrixError.html">MatrixError</a></td><td><span class="undocumented">Undocumented</span></td></tr><tr class="class"><td>Class</td><td><a href="sympy.matrices.matrices._MatrixAsBasic.html">_MatrixAsBasic</a></td><td><div><p>Proxy between Matrix &amp; Basic</p>
</div></td></tr><tr class="class"><td>Class</td><td><a href="sympy.matrices.matrices.Matrix.html">Matrix</a></td><td><span class="undocumented">Undocumented</span></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.matrices.matrices.zero">zero</a></td><td><div><p>Create square zero matrix n x n</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.matrices.matrices.zeronm">zeronm</a></td><td><div><p>Create zero matrix n x m</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.matrices.matrices.one">one</a></td><td><div><p>Create square all-one matrix n x n</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.matrices.matrices.eye">eye</a></td><td><div><p>Create square identity matrix n x n</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.matrices.matrices.randMatrix">randMatrix</a></td><td><div><p>Create random matrix r x c</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.matrices.matrices.hessian">hessian</a></td><td><div><p>Compute Hessian matrix for a function f</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.matrices.matrices.GramSchmidt">GramSchmidt</a></td><td><span class="undocumented">Undocumented</span></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.matrices.matrices.wronskian">wronskian</a></td><td><div><p>Compute wronskian for [] of functions</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.matrices.matrices.casoratian">casoratian</a></td><td><div><p>Given linear difference operator L of order 'k' and homogeneous</p>
</div></td></tr><tr class="class"><td>Class</td><td><a href="sympy.matrices.matrices.SMatrix.html">SMatrix</a></td><td><div><p>Sparse matrix</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.matrices.matrices.list2numpy">list2numpy</a></td><td><div><p>Converts python list of SymPy expressions to a NumPy array.</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.matrices.matrices.matrix2numpy">matrix2numpy</a></td><td><div><p>Converts SymPy's matrix to a NumPy array.</p>
</div></td></tr></table>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.matrices.matrices.zero">zero(n):</a></div>
            <div class="functionBody"><div><p>Create square zero matrix n x n</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.matrices.matrices.zeronm">zeronm(n, m):</a></div>
            <div class="functionBody"><div><p>Create zero matrix n x m</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.matrices.matrices.one">one(n):</a></div>
            <div class="functionBody"><div><p>Create square all-one matrix n x n</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.matrices.matrices.eye">eye(n):</a></div>
            <div class="functionBody"><div><p>Create square identity matrix n x n</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.matrices.matrices.randMatrix">randMatrix(r, c, min=0, max=99, seed=):</a></div>
            <div class="functionBody"><div><p>Create random matrix r x c</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.matrices.matrices.hessian">hessian(f, varlist):</a></div>
            <div class="functionBody"><div><p>Compute Hessian matrix for a function f</p>
<p>see: http://en.wikipedia.org/wiki/Hessian_matrix</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.matrices.matrices.GramSchmidt">GramSchmidt(vlist, orthog=False):</a></div>
            <div class="functionBody"><div class="undocumented">Undocumented</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.matrices.matrices.wronskian">wronskian(functions, var):</a></div>
            <div class="functionBody"><pre>Compute wronskian for [] of functions

               | f1    f2     ...   fn  |
               | f1'   f2'    ...   fn' |
               |  .     .     .      .  |
W(f1,...,fn) = |  .     .      .     .  |
               |  .     .       .    .  |
               |  n     n           n   |
               | D(f1) D(f2)  ...  D(fn)|

see: http://en.wikipedia.org/wiki/Wronskian</pre></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.matrices.matrices.casoratian">casoratian(seqs, n, zero=True):</a></div>
            <div class="functionBody"><pre>Given linear difference operator L of order 'k' and homogeneous
equation Ly = 0 we want to compute kernel of L, which is a set
of 'k' sequences: a(n), b(n), ... z(n).

Solutions of L are lineary independent iff their Casoratian,
denoted as C(a, b, ..., z), do not vanish for n = 0.

Casoratian is defined by k x k determinant:

           +  a(n)     b(n)     . . . z(n)     +
           |  a(n+1)   b(n+1)   . . . z(n+1)   |
           |    .         .     .        .     |
           |    .         .       .      .     |
           |    .         .         .    .     |
           +  a(n+k-1) b(n+k-1) . . . z(n+k-1) +

It proves very useful in rsolve_hyper() where it is applied
to a generating set of a recurrence to factor out lineary
dependent solutions and return a basis.

>>> from sympy import *
>>> n = Symbol('n', integer=True)

Exponential and factorial are lineary independent:

>>> casoratian([2**n, factorial(n)], n) != 0
True</pre></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.matrices.matrices.list2numpy">list2numpy(l):</a></div>
            <div class="functionBody"><div><p>Converts python list of SymPy expressions to a NumPy array.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.matrices.matrices.matrix2numpy">matrix2numpy(m):</a></div>
            <div class="functionBody"><div><p>Converts SymPy's matrix to a NumPy array.</p>
</div></div>
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